few_shots: Example:
Problem/activity:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Mathematical concept/skill options: 
A. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
C. Use equivalent fractions as a strategy to add and subtract fractions.
D. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
E. Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
F. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Thought: This problem involves understanding fractions as numbers by comparing their quantities.
Answer: F

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_000157

3
options: Understand the relationship between zeros and factors of polynomials.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Multiply and divide within 100.

Use polynomial identities to solve problems.

Use the four operations with whole numbers to solve problems.

Interpret the structure of expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Write expressions in equivalent forms to solve problems.

Write and interpret numerical expressions.

Use properties of operations to generate equivalent expressions.

Work with equal groups of objects to gain foundations for multiplication.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Reason about and solve one-variable equations and inequalities.

Represent and solve problems involving addition and subtraction.

Add and subtract within 20.

Work with addition and subtraction equations.

Understand and apply properties of operations and the relationship between addition and subtraction.

Understand solving equations as a process of reasoning and explain the reasoning.

Solve equations and inequalities in one variable.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Represent and solve problems involving multiplication and division.

Understand the connections between proportional relationships, lines, and linear equations.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Solve systems of equations.

Understand properties of multiplication and the relationship between multiplication and division.

Rewrite rational expressions.

Represent and solve equations and inequalities graphically.

Create equations that describe numbers or relationships

Apply and extend previous understandings of arithmetic to algebraic expressions.

Analyze patterns and relationships.

Work with radicals and integer exponents.

Perform arithmetic operations on polynomials.

Generate and analyze patterns.

Gain familiarity with factors and multiples.
problem_activity: Activity
Students use scientific notation as a tool to understand the relative scale of different units (MP2). They practice modeling skills by identifying essential elements of the problems and gathering relevant information before computing (MP4).
Launch
Arrange students in groups of 2. Instruct students to first read through the problems and decide on what information they need to solve each problem. Record relevant information for all students to see. Only record information when students have asked for it. Possible information students will ask for include:
Mai’s dad’s computer holds 500 gigabytes of storage space.
A kilobyte is 1,000 bytes, a megabyte is 1,000,000 bytes, and a gigabyte is 1,000,000,000 bytes.
1 character is roughly 1 byte.
An emoji is roughly 4 bytes.
A full-length, high-definition film is around 8 gigabytes and runs 2 hours.
A person sleeps about 8 hours in a night.
Give 15–20 minutes of work time before a brief whole-class discussion.
Representation: Internalize Comprehension.
Activate or supply background knowledge of working with very large numbers. Allow students to use calculators to ensure inclusive participation in the activity.
Supports accessibility for: Memory; Conceptual processing
Student Facing
For each question, think about what information you would need to figure out an answer. Your teacher may provide some of the information you ask for. Give your answers using scientific notation.
Mai found an 80’s computer magazine with an advertisement for a machine with hundreds of kilobytes of storage! Mai was curious and asked, “How many kilobytes would my dad’s new 2016 computer hold?”
The old magazine showed another ad for a 750-kilobyte floppy disk, a device used in the past to store data. How many gigabytes is this?
Mai and her friends are actively involved on a social media service that limits each message to 140 characters. She wonders about how the size of a message compares to other media.
Estimate how many messages it would take for Mai to fill up a floppy disk with her 140-character messages. Explain or show your reasoning.
Estimate how many messages it would take for Mai to fill a floppy disk with messages that only use emojis (each message being 140 emojis). Explain or show your reasoning.
Mai likes to go to the movies with her friends and knows that a high-definition film takes up a lot of storage space on a computer.
Estimate how many floppy disks it would take to store a high-definition movie. Explain or show your reasoning.
How many seconds of a high-definition movie would one floppy disk be able to hold?
If you fall asleep watching a movie streaming service and it streams movies all night while you sleep, how many floppy disks of information would that be?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
Humans tend to work with numbers using powers of 10, but computers work with numbers using powers of 2. A “binary kilobyte” is 1,024 bytes instead of 1,000, because
\(1,\!024 = 2^{10}\)
. Similarly, a “binary megabyte” is 1,024 binary kilobytes, and a “binary gigabyte” is 1,024 binary megabytes.
Which is bigger, a binary gigabyte or a regular gigabyte? How many more bytes is it?
Which is bigger, a binary terabyte or a regular terabyte? How many more bytes is it?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Activity Synthesis
In a whole-class discussion, ask students what they might have found surprising or interesting when comparing different digital media and different hardware. If time permits, discuss how scientific notation helps to make those comparisons.
Speaking: MLR8 Discussion Supports.
As students explain what they noticed about the differences in digital media and hardware, press for details in students’ ideas by requesting that students challenge an idea, elaborate on an idea, or make explicit their process for calculating or comparing the values. Revoice student ideas to model mathematical language use in order to clarify, apply appropriate language, and involve more students. This will help students produce and make sense of the language needed to communicate their own ideas.
Design Principle(s): Support sense-making; Optimize output (for explanation)


correct_option_index: 30